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The use of solid boron hydride molecules as a fuel for proton-boron fusion was proposed by M. Kr\r{u}s and M. Londesborough at "Interaction of Inorganic Clusters, Cages, and Containers with Light" workshop in November 2021. Here we demonstrate experimentally, for first time, that the solid boron hydride, octadecaborane - \textit{anti}-B${}_{18}$H${}_{22}$, produces a relatively high yield of alpha particles of about $10^9$ per steradian using a sub-nanosecond, low-contrast laser pulse (PALS) with a typical intensity of $10^{16}$ Wcm${}^{-2}$. In contrast to previously published proton-boron studies, the boron hydrides, due to their composition containing only atoms of boron and hydrogen, represent a natural choice for future proton-boron nuclear fusion schemes., Comment: 17 pages, 6 figures

We draw a parallel between the BV/BRST formalism for higher-dimensional ($\ge 2$) Hamiltonian mechanics and higher notions of torsion and basic curvature tensors for generalized connections in specific Lie $n$-algebroids based on homotopy Poisson structures. The gauge systems we consider include Poisson sigma models in any dimension and ``generalised R-flux'' deformations thereof, such as models with an $(n+2)$-form-twisted R-Poisson target space. Their BV/BRST action includes interaction terms among the fields, ghosts and antifields whose coefficients acquire a geometric meaning by considering twisted Koszul multibrackets that endow the target space with a structure that we call a gapped almost Lie $n$-algebroid. Studying covariant derivatives along $n$-forms, we define suitable polytorsion and basic polycurvature tensors and identify them with the interaction coefficients in the gauge theory, thus relating models for topological $n$-branes to differential geometry on Lie $n$-algebroids., Comment: 37 pages

The term life sciences refers to the disciplines that study living organisms and life processes, and include chemistry, biology, medicine, and a range of other related disciplines. Research efforts in life sciences are heavily data-driven, as they produce and consume vast amounts of scientific data, much of which is intrinsically relational and graph-structured. The volume of data and the complexity of scientific concepts and relations referred to therein promote the application of advanced knowledge-driven technologies for managing and interpreting data, with the ultimate aim to advance scientific discovery. In this survey and position paper, we discuss recent developments and advances in the use of graph-based technologies in life sciences and set out a vision for how these technologies will impact these fields into the future. We focus on three broad topics: the construction and management of Knowledge Graphs (KGs), the use of KGs and associated technologies in the discovery of new knowledge, and the use of KGs in artificial intelligence applications to support explanations (explainable AI). We select a few exemplary use cases for each topic, discuss the challenges and open research questions within these topics, and conclude with a perspective and outlook that summarizes the overarching challenges and their potential solutions as a guide for future research., Comment: 33 pages, 1 figure, camera-ready version, accepted for Transactions on Graph Data and Knowledge (TGDK)

We present an elementary construction of a (highly degenerate) Hopf pairing between the universal enveloping algebra $U(\mathfrak{g})$ of a finite-dimensional Lie algebra $\mathfrak{g}$ over arbitrary field $\mathbf{k}$ and the Hopf algebra $\mathcal{O}(\mathrm{Aut}(\mathfrak{g}))$ of regular functions on the automorphism group of $\mathfrak{g}$. This pairing induces a Hopf action of $\mathcal{O}(\mathrm{Aut}(\mathfrak{g}))$ on $U(\mathfrak{g})$ which together with an explicitly given coaction makes $U(\mathfrak{g})$ into a braided commutative Yetter--Drinfeld $\mathcal{O}(\mathrm{Aut}(\mathfrak{g}))$-module algebra. From these data one constructs a Hopf algebroid structure on the smash product algebra $\mathcal{O}(\mathrm{Aut}(\mathfrak{g}))\sharp U(\mathfrak{g})$ retaining essential features from earlier constructions of a Hopf algebroid structure on infinite-dimensional versions of Heisenberg double of $U(\mathfrak{g})$, including a noncommutative phase space of Lie algebra type, while avoiding the need of completed tensor products. We prove a slightly more general result where algebra $\mathcal{O}(\mathrm{Aut}(\mathfrak{g}))$ is replaced by $\mathcal{O}(\mathrm{Aut}(\mathfrak{h}))$ and where $\mathfrak{h}$ is any finite-dimensional Leibniz algebra having $\mathfrak{g}$ as its maximal Lie algebra quotient., Comment: v2: 18 pages, title slightly changed, presentation thoroughly revised

A class of left bialgebroids whose underlying algebra $A\sharp H$ is a smash product of a bialgebra $H$ with a braided commutative Yetter--Drinfeld $H$-algebra $A$ has recently been studied in relation to models of field theories on noncommutative spaces. In [A. Borowiec, A. Pachol, ``Twisted bialgebroids versus bialgebroids from a Drinfeld twist'', J. Phys. A50 (2017) 055205] a proof has been presented that the bialgebroid $A_F\sharp H^F$ where $H^F$ and $A_F$ are the twists of $H$ and $A$ by a Drinfeld 2-cocycle $F = \sum F^1\otimes F^2$ is isomorphic to the twist of the bialgebroid $A\sharp H$ by the bialgebroid 2-cocycle $\sum 1\sharp F^1\otimes 1\sharp F^2$ induced by $F$. They assume $H$ is quasitriangular, which is reasonable for many physical applications. However the proof and the entire paper take for granted that the coaction and the prebraiding are both given by special formulas involving the R-matrix. There are counterexamples of Yetter--Drinfeld modules over quasitriangular Hopf algebras which are not of this special form. Nevertheless, the main result essentially survives. We present a proof with general coaction and the correct prebraiding, and even without the assumption of quasitriangularity., Comment: v2: 10 pages, improved presentation, in particular more structured exposition in Sec. 2 and 3. Added Concluding remarks (Sec. 4) and few references. To appear in J. Phys. A

This study investigates the flow field induced by a surface dielectric barrier discharge (SDBD) system, known for its efficient pollution remediation of volatile organic compounds (VOCs). We aim to understand the flow dynamics that contribute to the high conversion observed in similar systems. Experimental techniques, including schlieren imaging and particle image velocimetry (PIV), applied with high temporal resolution, were used to analyse the flow field. Complementary, fluid simulations are employed to investigate the coupling between streamer and gas dynamics. Results show distinct fluid field behaviours for different electrode configurations, which differ in geometric complexity. The fluid field analysis of the most basic electrode design revealed behaviours commonly observed in actuator studies. The simulation results indicate the local information about the electron density as well as different temporal phases of the fluid flow. The electrode design with mostly parallel grid line structures exhibits confined vortices near the surface. In contrast, an electrode design also used in previous studies, is shown to promote strong gas transport through extended vortex structures, enhancing gas mixing and potentially explaining the high conversion observed., Comment: submitted to Plasma Chemistry and Plasma Processing by Springer Nature

We generalize the notion of convexity and average-convexity to the notion of weighted average-convexity. We show several results on the relation between weighted average-convexity and cooperative games. First, we prove that if a game is weighted average-convex, then the corresponding weighted Shapley value is in the core. Second, we exhibit necessary conditions for a communication TU-game to preserve the weighted average-convexity. Finally, we provide a complete characterization when the underlying graph is a priority decreasing tree.

Symmetric ordering and Weyl realizations for non commutative quantum Minkowski spaces are reviewed. Weyl realizations of Lie deformed spaces and corresponding star products, as well as twist corresponding to Weyl realization and coproduct of momenta are presented. Drinfeld twists understood in Hopf algebroid sense are also discussed. A few examples of corresponding Weyl realizations are given. We show that for the original Snyder space there exists symmetric ordering, but no Weyl realization. Quadratic deformations of Minkowski space are considered and it is demonstrated that symmetric ordering is deformed and a generalized Weyl realization can be defined., Comment: 25 pages, to appear in J. Math. Physics

The estimation of fluid flows inside a centrifugal pump in realtime is a challenging task that cannot be achieved with long-established methods like CFD due to their computational demands. We use a projection-based reduced order model (ROM) instead. Based on this ROM, a realtime observer can be devised that estimates the temporally and spatially resolved velocity and pressure fields inside the pump. The entire fluid-solid domain is treated as a fluid in order to be able to consider moving rigid bodies in the reduction method. A greedy algorithm is introduced for finding suitable and as few measurement locations as possible. Robust observability is ensured with an extended Kalman filter, which is based on a time-variant observability matrix obtained from the nonlinear velocity ROM. We present the results of the velocity and pressure ROMs based on a unsteady Reynolds-averaged Navier-Stokes CFD simulation of a 2D centrifugal pump, as well as the results for the extended Kalman filter., Comment: 20 pages, 12 figures

The results of the first synoptic survey of novae in the barred spiral and starburst galaxy, M83 (NGC 5236), are presented. A total of 19 novae and one background supernova were discovered during the course of a nearly seven-year survey comprised of over 200 individual nights of observation between 2012 December 12 and 2019 March 14. After correcting for the limiting magnitude and the spatial and temporal coverage of the survey, the nova rate in M83 was found to be $R=19^{+5}_{-3}$ yr$^{-1}$. This rate, when normalized to the $K$-band luminosity of the galaxy, yields a luminosity-specific nova rate, $\nu_K = 3.0^{+0.9}_{-0.6}\times10^{-10}$ yr$^{-1} L_{\odot,K}^{-1}$. The spatial distribution of the novae is found to be more extended than the overall galaxy light suggesting that the observed novae are likely dominated by a disk population. This result is consistent with the observed nova light curves which reveal that the M83 novae are on average more luminous at maximum light and fade faster when compared with novae observed in M31. Generally, the more luminous M83 novae were observed to fade more rapidly, with the complete sample being broadly consistent with a linear Maximum-Magnitude vs Rate of Decline relation., Comment: 24 pages, 12 figures, accepted for publication in the Astrophysical Journal

We argue that there is a hierarchy of levels describing to that particular level relevant features of reality behind the content and behavior of blockchain and smart contracts in their realistic deployment. Choice, design, audit and legal control of these systems could be more informed, easier and raised to a higher level, if research on foundations of these descriptions develops and sets the formalisms, tools and standards for such descriptions., Comment: early draft, to be significantly expanded

We introduce the generalized Heisenberg algebra appropriate for realizations of the $\mathfrak{gl}(n)$ algebra. Linear realizations of the $\mathfrak{gl}(n)$ algebra are presented and the corresponding star product, coproduct of momenta and twist are constructed. The dual realization and dual $\mathfrak{gl}(n)$ algebra are considered. Finally, we present a general realization of the $\mathfrak{gl}(n)$ algebra, the corresponding coproduct of momenta and two classes of twists. These results can be applied to physical theories on noncommutative spaces of the $\mathfrak{gl}(n)$ type.

Current archives of the LAMOST telescope contain millions of pipeline-processed spectra that have probably never been seen by human eyes. Most of the rare objects with interesting physical properties, however, can only be identified by visual analysis of their characteristic spectral features. A proper combination of interactive visualisation with modern machine learning techniques opens new ways to discover such objects. We apply active learning classification supported by deep convolutional networks to automatically identify complex emission-line shapes in multi-million spectra archives. We used the pool-based uncertainty sampling active learning driven by a custom-designed deep convolutional neural network with 12 layers inspired by VGGNet, AlexNet, and ZFNet, but adapted for one-dimensional feature vectors. The unlabelled pool set is represented by 4.1 million spectra from the LAMOST DR2 survey. The initial training of the network was performed on a labelled set of about 13000 spectra obtained in the region around H$\alpha$ by the 2m Perek telescope of the Ond\v{r}ejov observatory, which mostly contains spectra of Be and related early-type stars. The differences between the Ond\v{r}ejov intermediate-resolution and the LAMOST low-resolution spectrographs were compensated for by Gaussian blurring. After several iterations, the network was able to successfully identify emission-line stars with an error smaller than 6.5%. Using the technology of the Virtual Observatory to visualise the results, we discovered 1013 spectra of 948 new candidates of emission-line objects in addition to 664 spectra of 549 objects that are listed in SIMBAD and 2644 spectra of 2291 objects identified in an earlier paper of a Chinese group led by Wen Hou. The most interesting objects with unusual spectral properties are discussed in detail., Comment: To appear in Astronomy & Astrophysics Section 14- Catalogs and Data, 15 pages, 13 figures

We consider a restricted game on weighted graphs associated with minimum partitions. We replace in the classical definition of Myerson restricted game the connected components of any subgraph by the sub-components obtained with a specific partition $\tilde{\mathcal{P}}_{\min}$. This partition relies on the same principle as the partition $\mathcal{P}_{\min}$ introduced by Grabisch and Skoda (2012) but restricted to connected coalitions. More precisely, this new partition $\tilde{\mathcal{P}}_{\min}$ is induced by the deletion of the minimum weight edges in each connected component associated with a coalition. We provide a characterization of the graphs satisfying inheritance of convexity from the underlying game to the restricted game associated with $\tilde{\mathcal{P}}_{\min}$.

We consider a bounded open Stein subset $\Omega$ of a complex Stein manifold $X$ of dimension $n$. We prove that if $f$ is a current on $X$ of bidegree $(p,q+1)$, $\bar\partial$-closed on $\Omega$, we can find a current $u$ on $X$ of bidegree $(p,q)$ which is a solution of the equation $\bar\partial u=f$ in $\Omega$. In other words, we prove that the Dolbeault complex of temperate currents on $\Omega$ (i.e. currents on $\Omega$ which extend to currents on $X$) is concentrated in degree $0$. Moreover if $f$ is a current on $X= C^n$ of order $k$, then we can find a solution $u$ which is a current on $C^n$ of order $k+2n+1$.

We consider two families of Drinfeld twists generated from a simple Jordanian twist further twisted with 1-cochains. Using combinatorial identities, they are presented as a series expansion in the dilatation and momentum generators. These twists interpolate between two simple Jordanian twists. For an expansion of a family of twists $\mathcal{F}_{L,u}$, we also show directly that the 2-cocycle condition reduces to previously proven identities., Comment: 11 pages, continuation of our earlier work arXiv:1904.03993, SIGMA 15 (2019) 082

Graphs that are critical (minimal excluded minors) for embeddability in surfaces are studied. In Part I, it was shown that graphs that are critical for embeddings into surfaces of Euler genus $k$ or for embeddings into nonorientable surface of genus $k$ are built from 3-connected components, called hoppers and cascades. In Part II, all cascades for Euler genus 2 are classified. As a consequence, the complete list of obstructions of connectivity 2 for embedding graphs into the Klein bottle is obtained., Comment: The original paper arxiv:1406.1341 was split into two parts, this is Part II

Graphs that are critical (minimal excluded minors) for embeddability in surfaces are studied. In Part I we consider the structure of graphs with a 2-vertex-cut that are critical with respect to the Euler genus. A general theorem describing the building blocks is presented. These constituents, called hoppers and cascades, are classified for the case when Euler genus is small. As a consequence, the complete list of obstructions of connectivity 2 for embedding graphs into the Klein bottle is obtained. This is the first complete result about obstructions for embeddability of graphs in the Klein bottle, and the outcome is somewhat surprising in the sense that there are considerably fewer excluded minors than expected., Comment: The full paper that was originally arXiv:1406.1341 has been split into two parts. This is Part I

Let $\hat{A}_n$ be the completion by the degree of a differential operator of the $n$-th Weyl algebra with generators $x_1,\ldots,x_n,\partial^1,\ldots,\partial^n$. Consider $n$ elements $X_1,\ldots,X_n$ in $\hat{A}_n$ of the form $$ X_i = x_i + \sum_{K = 1}^\infty \sum_{l = 1}^n\sum_{j = 1}^n x_l p_{ij}^{K-1,l}(\partial)\partial^j, $$ where $p^{K-1,l}_{ij}(\partial)$ is a degree $(K-1)$ homogeneous polynomial in $\partial^1,\ldots,\partial^n$, antisymmetric in subscripts $i,j$. Then for any natural $k$ and any function $i : \{1,\ldots,k\}\to\{1,\ldots,n\}$ we prove $$ \sum_{\sigma \in \Sigma(k)} X_{i_{\sigma(1)}}\cdots X_{i_{\sigma(k)}}\triangleright 1 = k! \,x_{i_1}\cdots x_{i_k}, $$ where $\Sigma(k)$ is the symmetric group on $k$ letters and $\triangleright$ denotes the Fock action of the $\hat{A}_n$ on the space of (commutative) polynomials., Comment: 8 pages, v2: expositional improvements and corrections; the second half of the main theorem's proof written much more explicitly

Fulfilling the goals of space-based exoplanetary transit surveys, like Kepler and TESS, is impossible without ground-based spectroscopic follow-up. In particular, the first-step vetting of candidates could easily necessitate several hundreds of hours of telescope time -- an area where 2-m class telescopes can play a crucial role. Here, we describe the results from the science verification of the Ond\v{r}ejov Echelle Spectrograph (OES) installed on the 2-m Perek telescope. We discuss the performance of the instrument as well as its suitability for the study of exoplanetary candidates from space-based transit surveys. In spite of being located at an average European observing site, and originally being conceived for the study of variable stars, OES can prove to be an important instrument for the exoplanetary community in the TESS and PLATO era -- reaching accuracies of a few tens of m/s with reasonable sampling and signal-to-noise for sources down to V$\sim$13. The stability of OES is demonstrated via long-term monitoring of the standard star HD~109358, while its validity for exoplanetary candidate verification is shown using three K2 candidates EPIC~210925707, EPIC~206135267 and EPIC~211993818, to reveal that they are false positive detections., Comment: accepted for publication in PASP

We consider a two parameter family of Drinfeld twists generated from a simple Jordanian twist further twisted by 1-cochains. Twists from this family interpolate between two simple Jordanian twists. Relations between them are constructed and discussed. It is proved that there exists a one parameter family of twists identical to a simple Jordanian twist. The twisted coalgebra, star product and coordinate realizations of the $\kappa$-Minkowski noncommutative space time are presented. Real forms of Jordanian deformations are also discussed. The method of similarity transformations is applied to the Poincar\'e-Weyl Hopf algebra and two types of one parameter families of dispersion relations are constructed. Mathematically equivalent deformations, that are related to nonlinear changes of symmetry generators and linked with similarity maps, may lead to differences in the description of physical phenomena., Comment: to be published in Int. J. Mod. Phys. A

Reliable determination of the basic physical properties of hot emission-line binaries with Roche-lobe filling secondaries is important for developing the theory of mass exchange in binaries. It is not easy, however, due to the presence of circumstellar matter. Here, we report the first detailed investigation of a new representative of this class of binaries, HD~81357, based on the analysis of spectra and photometry from several observatories. HD~81357 was found to be a double-lined spectroscopic binary and an ellipsoidal variable seen under an intermediate orbital inclination of $\sim(63\pm5)^\circ$, having an orbital period of 33\fd77445(41) and a~circular orbit. From an automated comparison of the observed and synthetic spectra, we estimate the component's effective temperatures to be 12930(540)~K and 4260(24)~K. The combined light-curve and orbital solutions, also constrained by a very accurate Gaia Data Release 2 parallax, give the following values of the basic physical properties: masses $3.36\pm0.15$ and $0.34\pm0.04$~\Mnom, radii $3.9\pm0.2$ and 13.97\pm0.05$~\Rnom, and a~mass ratio $10.0\pm0.5$. Evolutionary modelling of the system including the phase of mass transfer between the components indicated that HD~81357 is a~system observed in the final slow phase of the mass exchange after the mass-ratio reversal. Contrary to what has been seen for similar binaries like AU~Mon, no cyclic light variations were found on a~time scale an~order of magnitude longer than the orbital period. 243,1 15%, Comment: 16 pages, 9 figures; accepted for publication in Astronomy and Astrophysics

We propose an explicit generalization of the Jordanian twist proposed in $r$-symmetrized form by Giaquinto and Zhang. It is proved that this generalization satisfies the 2-cocycle condition. We present explicit formulas for the corresponding star product and twisted coproduct. Finally, we show that our generalization coincides with the twist obtained from the simple Jordanian twist by twisting by a 1-cochain.

Protein adsorption at the solid-liquid interface is an important phenomenon that often can be observed as a first step in biological processes. Despite its inherent importance, still relatively little is known about the underlying microscopic mechanisms. Here, using multivalent ions, we demonstrate the control of the interactions and the corresponding adsorption of net-negatively charged proteins (bovine serum albumin) at a solid-liquid interface. This is demonstrated by ellipsometry and corroborated by neutron reflectivity and quartz-crystal microbalance experiments. We show that the reentrant condensation observed within the rich bulk phase behavior of the system featuring a nonmonotonic dependence of the second virial cofficient on salt concentration c_s is reflected in an intriguing way in the protein adsorption d(c_s) at the interface. Our findings are successfully described and understood by a model of ion-activated patchy interactions within the framework of classical density functional theory. In addition to the general challenge of connecting bulk and interface behavior, our work has implications for, inter alia, nucleation at interfaces., Comment: 5 pages, 3 Figures, accepted by Phys. Rev. Lett

We consider restricted games on weighted graphs associated with minimum partitions. We replace in the classical definition of Myerson restricted game the connected components of any subgraph by the subcomponents corresponding to a minimum partition. This minimum partition $\mathcal{P}_{\min}$ is induced by the deletion of the minimum weight edges. We provide a characterization of the graphs satisfying inheritance of convexity from the underlying game to the restricted game associated with Pmin. Moreover, we prove that these graphs can be recognized in polynomial time.

The purpose of this document is to create a data model and its serialization for expressing generic time series data. Already existing IVOA data models are reused as much as possible. The model is also made as generic as possible to be open to new extensions but at the same time closed for modifications. This enables maintaining interoperability throughout different versions of the data model. We define the necessary building blocks for metadata discovery, serialization of time series data and understanding it by clients. We present several categories of time series science cases with examples of implementation. We also take into account the most pressing topics for time series providers like tracking original images for every individual point of a light curve or time-derived axes like frequency for gravitational wave analysis. The main motivation for the creation of a new model is to provide a unified time series data publishing standard - not only for light curves but also more generic time series data, e.g., radial velocity curves, power spectra, hardness ratio, provenance linkage, etc. The flexibility is the most crucial part of our model - we are not dependent on any physical domain or frame models. While images or spectra are already stable and standardized products, the time series related domains are still not completely evolved and new ones will likely emerge in near future. That is why we need to keep models like Time Series Cube DM independent of any underlying physical models. In our opinion, this is the only correct and sustainable way for future development of IVOA standards., Comment: 30 pages, 17 figures

The LAMOST DR1 survey contains about two million of spectra labelled by its pipeline as stellar objects of common spectral classes. There is, however, a lot of spectra corrupted in some way by both instrumental and processing artifacts, which may mimic spectral properties of interesting celestial objects, namely emission lines of Be stars and quasars. We have tested several clustering methods as well as outliers analysis on a sample of one hundred thousand spectra using Spark scripts running on Hadoop cluster consisting of twenty-four sixteen-core nodes. This experiment was motivated by an attempt to find rare objects with interesting spectra as outliers most dissimilar from all common spectra. The result of this time-consuming procedure is a list of several hundred candidates where different artifacts are prominent, but also tens of very interesting emission-line spectra requiring further detailed examination. Many of them may be quasars or even blazars as well as yet unknown Be-stars. It deserves mentioning that most of the work benefitted considerably from technologies of Virtual Observatory., Comment: 4 pages, 2 figures. To appear in the proceedings of the Astronomical Data Analysis Software and Systems XXVI (ADASS XXVI)

The current archives of LAMOST multi-object spectrograph contain millions of fully reduced spectra, from which the automatic pipelines have produced catalogues of many parameters of individual objects, including their approximate spectral classification. This is, however, mostly based on the global shape of the whole spectrum and on integral properties of spectra in given bandpasses, namely presence and equivalent width of prominent spectral lines, while for identification of some interesting object types (e.g. Be stars or quasars) the detailed shape of only a few lines is crucial. Here the machine learning is bringing a new methodology capable of improving the reliability of classification of such objects even in boundary cases. We present results of Spark-based semi-supervised machine learning of LAMOST spectra attempting to automatically identify the single and double-peak emission of H alpha line typical for Be and B[e] stars. The labelled sample was obtained from archive of 2m Perek telescope at Ond\v{r}ejov observatory. A simple physical model of spectrograph resolution was used in domain adaptation to LAMOST training domain. The resulting list of candidates contains dozens of Be stars (some are likely yet unknown), but also a bunch of interesting objects resembling spectra of quasars and even blazars, as well as many instrumental artefacts. The verification of a nature of interesting candidates benefited considerably from cross-matching and visualisation in the Virtual Observatory environment., Comment: 6 pages, 5 figures, Accepted for Proceedings of IAU Symposium 325 (Astroinformatics 2016)

Recently, S. Meljanac proposed a construction of a class of examples of an algebraic structure with properties very close to the Hopf algebroids $H$ over a noncommutative base $A$ of other authors. His examples come along with a subalgebra $\mathcal{B}$ of $H\otimes H$, here called the balancing subalgebra, which contains the image of the coproduct and such that the intersection of $\mathcal{B}$ with the kernel of the projection $H\otimes H\to H\otimes_A H$ is a two-sided ideal in $\mathcal{B}$ which is moreover well behaved with respect to the antipode. We propose a set of abstract axioms covering this construction and make a detailed comparison to the Hopf algebroids of Lu. We prove that every scalar extension Hopf algebroid can be cast into this new set of axioms. We present an observation by G. B\"ohm that the Hopf algebroids constructed from weak Hopf algebras fit into our framework as well. At the end we discuss the change of balancing subalgebra under Drinfeld-Xu procedure of twisting of associative bialgebroids by invertible 2-cocycles., Comment: v3 accepted version; v2 old title A two sided ideal in Hopf algebroid axiomatics changed to Hopf algebroids with balancing subalgebra; thoroughly revised and extended from 18 to 29 pages, entirely new sections on weak Hopf algebras and on Drinfeld-Xu twists (the first submission to a journal planned within days, but suggestions still welcome)